Light emitting diodes (LEDs) having a semiconductor light generation region situated on a light absorbing substrate are widely used as light sources and are beginning to replace incandescent lamps. In order to meet the demands for light output, it is important that the overall light output efficiency of the LEDs be maximized. One improvement made in the prior art, disclosed in U.S. Pat. No. 5,008,718, has been to increase the LED electrical efficiency by including a thin electrically conductive transparent window layer between the light generation region and the top metal contact so that current crowding is minimized. An unfortunate shortcoming of the thin window layer has been that a significant portion of the total light generated by the light generation region is still internally reflected within the window layer and is absorbed by the substrate instead of being emitted out of the LED.